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math.DG2026
Boundary behaviour of stable Allen-Cahn limit-interfaces in Riemannian manifolds
Martin Man-chun Li, Davide Parise, Lorenzo Sarnataro
This is the second paper in our series of works to develop the min-max theory for free boundary minimal hypersurfaces in Riemannian manifolds with boundary via the Allen-Cahn equat…
math.DG2026
White's cone over the Möbius band is area-minimising
Marco A. M. Guaraco, Davide Parise
We prove that the cone in over a suitable minimal Möbius band is locally mass-minimising with coefficients in . This proves…
math.DG2026
Uniqueness of free boundary minimal annuli
Davide Parise, Jonathan J. Zhu
We prove that every smooth properly embedded free-boundary minimal annulus in the unit ball is congruent to the critical catenoid. We also classify positive solutions of $(Δ_{\math…